Reading the Texture of Reality : Chaos Theory, Literature and the Humanist Perspective

Tutkimuksessa analysoidaan kaaosteorian vaikutusta kaunokirjallisuudessa ja kirjallisuudentutkimuksessa ja esitetään, että kaaosteorian roolia kirjallisuuden kentällä voidaan parhaiten ymmärtää sen avaamien käsitteiden kautta. Suoran soveltamisen sijaan kaaosteorian avulla on käyty uudenlaisia keskusteluja vanhoista aiheista ja luonnontieteestä ammennetut käsitteet ovat johtaneet aiemmin tukkeutuneiden argumenttien avaamiseen uudesta näkökulmasta käsin. Väitöskirjassa keskitytään kolmeen osa-alueeseen: kaunokirjallisen teoksen rakenteen teoretisointiin, ihmisen (erityisesti tekijän) identiteetin hahmottamiseen ja kuvailemiseen sekä fiktion ja todellisuuden suhteen pohdintaan. Tutkimuksen tarkoituksena on osoittaa, kuinka kaaosteorian kautta näitä aiheita on lähestytty niin kirjallisuustieteessä kuin kaunokirjallisissa teoksissakin. Väitöskirjan keskiössä ovat romaanikirjailija John Barthin, dramatisti Tom Stoppardin ja runoilija Jorie Grahamin teosten analyysit. Nämä kirjailijat ammentavat kaaosteoriasta keinoja käsitteellistää rakenteita, jotka ovat yhtä aikaa dynaamisia prosesseja ja hahmotettavia muotoja. Kaunokirjallisina teemoina nousevat esiin myös ihmisen paradoksaalisesti tunnistettava ja aina muuttuva identiteetti sekä lopullista haltuunottoa pakeneva, mutta silti kiehtova ja tavoiteltava todellisuus. Näiden kirjailijoiden teosten analyysin sekä teoreettisen keskustelun kautta väitöskirjassa tuodaan esiin aiemmassa tutkimuksessa varjoon jäänyt, koherenssia, ymmärrettävyyttä ja realismia painottava humanistinen näkökulma kaaosteorian merkityksestä kirjallisuudessa.

On the Epistemology of Narrative Theory: Narratology and Other Theories of Fictional Narrative

In this article, I propose to analyze narrative theory from an epistemological standpoint. To do so, I will draw upon both Genettian narratology and what I would call, following Shigeyuki Kuroda, “non-communicational” theories of fictional narrative. In spite of their very unequal popularity, I consider these theories as objective, or, in other words, as debatable and ripe for rational analyses; one can choose between them. The article is made up of three parts. The first part concerns the object of narrative theory, or the narrative as a constructed object, both in narratology (where narrative is likened to a narrative discourse) and in non-communicational narrative theories (where fictional narrative and discourse are mutually exclusive categories). The second part takes up the question of how the claims of these theories do or do not lend themselves to falsification. In particular, Gérard Genette’s claim that “every narrative is, explicitly or not, ‘in the first person’”, will be considered, through the lens of Ann Banfield’s theory of free indirect style. In the third part the reductionism of narrative theory will be dealt with. This leads to a reflection on the role of narrative theory in the analysis of fictional narratives.

Logic as the Universal Science : Bertrand Russell's Early Conception of Logic and Its Philosophical Context

Bertrand Russell (1872 1970) introduced the English-speaking philosophical world to modern, mathematical logic and foundational study of mathematics. The present study concerns the conception of logic that underlies his early logicist philosophy of mathematics, formulated in The Principles of Mathematics (1903). In 1967, Jean van Heijenoort published a paper, Logic as Language and Logic as Calculus, in which he argued that the early development of modern logic (roughly the period 1879 1930) can be understood, when considered in the light of a distinction between two essentially different perspectives on logic. According to the view of logic as language, logic constitutes the general framework for all rational discourse, or meaningful use of language, whereas the conception of logic as calculus regards logic more as a symbolism which is subject to reinterpretation. The calculus-view paves the way for systematic metatheory, where logic itself becomes a subject of mathematical study (model-theory). Several scholars have interpreted Russell s views on logic with the help of the interpretative tool introduced by van Heijenoort,. They have commonly argued that Russell s is a clear-cut case of the view of logic as language. In the present study a detailed reconstruction of the view and its implications is provided, and it is argued that the interpretation is seriously misleading as to what he really thought about logic. I argue that Russell s conception is best understood by setting it in its proper philosophical context. This is constituted by Immanuel Kant s theory of mathematics. Kant had argued that purely conceptual thought basically, the logical forms recognised in Aristotelian logic cannot capture the content of mathematical judgments and reasonings. Mathematical cognition is not grounded in logic but in space and time as the pure forms of intuition. As against this view, Russell argued that once logic is developed into a proper tool which can be applied to mathematical theories, Kant s views turn out to be completely wrong. In the present work the view is defended that Russell s logicist philosophy of mathematics, or the view that mathematics is really only logic, is based on what I term the Bolzanian account of logic . According to this conception, (i) the distinction between form and content is not explanatory in logic; (ii) the propositions of logic have genuine content; (iii) this content is conferred upon them by special entities, logical constants . The Bolzanian account, it is argued, is both historically important and throws genuine light on Russell s conception of logic.

On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

On linear order and computation : The expressiveness of interactive computations on linear orders and computations indexed by ordinals

We solve the Dynamic Ehrenfeucht-Fra\"iss\'e Game on linear orders for both players, yielding a normal form for quantifier-rank equivalence classes of linear orders in first-order logic, infinitary logic, and generalized-infinitary logics with linearly ordered clocks. We show that Scott Sentences can be manipulated quickly, classified into local information, and consistency can be decided effectively in the length of the Scott Sentence. We describe a finite set of linked automata moving continuously on a linear order. Running them on ordinals, we compute the ordinal truth predicate and compute truth in the constructible universe of set-theory. Among the corollaries are a study of semi-models as efficient database of both model-theoretic and formulaic information, and a new proof of the atomicity of the Boolean algebra of sentences consistent with the theory of linear order -- i.e., that the finitely axiomatized theories of linear order are dense.

Locality and order-invariant logics

Malli on logiikassa käytetty abstraktio monille matemaattisille objekteille. Esimerkiksi verkot, ryhmät ja metriset avaruudet ovat malleja. Äärellisten mallien teoria on logiikan osa-alue, jossa tarkastellaan logiikkojen, formaalien kielten, ilmaisuvoimaa malleissa, joiden alkioiden lukumäärä on äärellinen. Rajoittuminen äärellisiin malleihin mahdollistaa tulosten soveltamisen teoreettisessa tietojenkäsittelytieteessä, jonka näkökulmasta logiikan kaavoja voidaan ajatella ohjelmina ja äärellisiä malleja niiden syötteinä. Lokaalisuus tarkoittaa logiikan kyvyttömyyttä erottaa toisistaan malleja, joiden paikalliset piirteet vastaavat toisiaan. Väitöskirjassa tarkastellaan useita lokaalisuuden muotoja ja niiden säilymistä logiikkoja yhdistellessä. Kehitettyjä työkaluja apuna käyttäen osoitetaan, että Gaifman- ja Hanf-lokaalisuudeksi kutsuttujen varianttien välissä on lokaalisuuskäsitteiden hierarkia, jonka eri tasot voidaan erottaa toisistaan kasvavaa dimensiota olevissa hiloissa. Toisaalta osoitetaan, että lokaalisuuskäsitteet eivät eroa toisistaan, kun rajoitutaan tarkastelemaan äärellisiä puita. Järjestysinvariantit logiikat ovat kieliä, joissa on käytössä sisäänrakennettu järjestysrelaatio, mutta sitä on käytettävä siten, etteivät kaavojen ilmaisemat asiat riipu valitusta järjestyksestä. Määritelmää voi motivoida tietojenkäsittelyn näkökulmasta: vaikka ohjelman syötteen tietojen järjestyksellä ei olisi odotetun tuloksen kannalta merkitystä, on syöte tietokoneen muistissa aina jossakin järjestyksessä, jota ohjelma voi laskennassaan hyödyntää. Väitöskirjassa tutkitaan minkälaisia lokaalisuuden muotoja järjestysinvariantit ensimmäisen kertaluvun predikaattilogiikan laajennukset yksipaikkaisilla kvanttoreilla voivat toteuttaa. Tuloksia sovelletaan tarkastelemalla, milloin sisäänrakennettu järjestys lisää logiikan ilmaisuvoimaa äärellisissä puissa.

Marketing and the Logic of Service: Value Facilitation, Value Creation and Co-creation, and Their Marketing Implications

The discussion of a service-dominant logic has made the findings of decades of service marketing research a topic of interest for marketing at large. Some fundamental aspects of the logic such as value creation and its marketing implications are more complex than they have been treated as so far and need to be further developed to serve marketing theory and practice well. Following the analysis in the present article it is argued that although customers are co-producers in service processes, according to the value-in-use notion adopted in the contemporary marketing and management literature they are fundamentally the creators of value for themselves. Furthermore, it is concluded that although by providing goods and services as input resources into customers’ consumption and value-generating processes firms are fundamentally value facilitators, interactions with customers that exist or can be created enable firms to engage themselves with their customers’ processes and thereby they become co-creators of value with their customers. As marketing implications it is observed that 1) the goal of marketing is to support customers’ value creation, 2) following a service logic and due to the existence of interactions where the firm’s and the customer’s processes merge into an integrated joint value creation process, the firm is not restricted to making value propositions only, but can directly and actively influence the customer’s value fulfilment as well and extend its marketing process to include activities during customer-firm interactions, and 3) although all goods and services are consumed as service, customers’ purchasing decisions can be expected to be dependant of whether they have the skills and interest to use a resource, such as a good, as service or want to buy extended market offerings including process-related elements. Finally, the analysis concludes with five service logic theses.

Proofs, Paradoxes, and Probabilities : The Logical Turn of Philosophy in Finland

This monograph describes the emergence of independent research on logic in Finland. The emphasis is placed on three well-known students of Eino Kaila: Georg Henrik von Wright (1916-2003), Erik Stenius (1911-1990), and Oiva Ketonen (1913-2000), and their research between the early 1930s and the early 1950s. The early academic work of these scholars laid the foundations for today's strong tradition in logic in Finland and also became internationally recognized. However, due attention has not been given to these works later, nor have they been comprehensively presented together. Each chapter of the book focuses on the life and work of one of Kaila's aforementioned students, with a fourth chapter discussing works on logic by authors who would later become known within other disciplines. Through an extensive use of correspondence and other archived material, some insight has been gained into the persons behind the academic personae. Unique and unpublished biographical material has been available for this task. The chapter on Oiva Ketonen focuses primarily on his work on what is today known as proof theory, especially on his proof theoretical system with invertible rules that permits a terminating root-first proof search. The independency of the parallel postulate is proved as an example of the strength of root-first proof search. Ketonen was to our knowledge Gerhard Gentzen's (the 'father' of proof theory) only student. Correspondence and a hitherto unavailable autobiographic manuscript, in addition to an unpublished article on the relationship between logic and epistemology, is presented. The chapter on Erik Stenius discusses his work on paradoxes and set theory, more specifically on how a rigid theory of definitions is employed to avoid these paradoxes. A presentation by Paul Bernays on Stenius' attempt at a proof of the consistency of arithmetic is reconstructed based on Bernays' lecture notes. Stenius correspondence with Paul Bernays, Evert Beth, and Georg Kreisel is discussed. The chapter on Georg Henrik von Wright presents his early work on probability and epistemology, along with his later work on modal logic that made him internationally famous. Correspondence from various archives (especially with Kaila and Charlie Dunbar Broad) further discusses his academic achievements and his experiences during the challenging circumstances of the 1940s.

The Homeless Etiquette : Social Interaction and Behavior Among the Homeless in Taito Ward, Tokyo

The thesis focuses on the social interaction and behavior of the homeless living in Tokyo's Taito Ward. The study is based on the author's own ethnographic field research carried out in the autumn 2003. The chosen methodologies were based on the methodology called "participant observation", and they were used depending on the context. The ethnographic field research was carried out from the mid-August to the beginning of the October in 2003. The most important targets of the research were three separate loosely knit groups placed in certain parts of Taito Ward. One of these groups was based in proximity to the Ueno train station, one group gathered every morning around a homeless support organization called San'yûkai, and one was based in Tamahime Park located in the old San'ya area of Tokyo. The analysis is based on the aspects of Takie Sugiyama Lebra's theory of "social relativism". Lebra's theory consists of the following, arguably universal aspects: belongingness, empathy, dependence, place in the society, and reciprocity. In addition, all the interaction and behavior is tied to the context and the situation. According to Lebra, ritual and intimate situations produce similar action, which is socially relative. Of these, the norms of the ritual behavior are more regulated, while the intimate bahavior is less spontaneous. On the contrary, an anomic situation produces anomic behavior, which is not socially relative. Lebra's theory is critically reviewed by the author of the thesis, and the author has attempted to modify the theory to make it more adaptable to the present-day society and to the analysis. Erving Goffman's views of the social interaction and Anthony Giddens' theories about the social structures have been used as complementary thoretical basis. The aim of the thesis is to clarify, how and why the interaction and the behavior of some homeless individuals in some situations follow the aspects of Lebra's "social relativism", and on the other hand, why in some situations they do not. In the latter cases the answers can be sought from regional and individual differences, or from the inaptness of the theory to analyze the presented situation. Here, a significant factor is the major finding of the field study: the so called "homeless etiquette", which is an abstract set of norms and values that influences the social interaction and behavior of the homeless, and with which many homeless individuals presented in the study complied. The fundamental goal of the thesis is to reach profound understanding about the daily life of the homeless, whose lives were studied. The author argues that this kind of profound understanding is necessary in looking for sustainable solutions in the areas of social and housing policy to improve the position of the homeless and the qualitative functioning of the society.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

Convex-transitive Banach spaces and their hyperplanes

The topic of this dissertation is the geometric and isometric theory of Banach spaces. This work is motivated by the known Banach-Mazur rotation problem, which asks whether each transitive separable Banach space is isometrically a Hilbert space. A Banach space X is said to be transitive if the isometry group of X acts transitively on the unit sphere of X. In fact, some weaker symmetry conditions than transitivity are studied in the dissertation. One such condition is an almost isometric version of transitivity. Another investigated condition is convex-transitivity, which requires that the closed convex hull of the orbit of any point of the unit sphere under the rotation group is the whole unit ball. Following the tradition developed around the rotation problem, some contemporary problems are studied. Namely, we attempt to characterize Hilbert spaces by using convex-transitivity together with the existence of a 1-dimensional bicontractive projection on the space, and some mild geometric assumptions. The convex-transitivity of some vector-valued function spaces is studied as well. The thesis also touches convex-transitivity of Banach lattices and resembling geometric cases.

Profligate Descent : The Cultural Transformations of Evolutionary Narrative

This dissertation traces a set of historical transformations the Darwinian evolutionary narrative has undergone toward the end of the twentieth century, especially as reflected in Anglo-American popular science books and novels. The study has three objectives. First, it seeks to understand the organizing logic of evolutionary narratives and the role that assumptions about gender and sexuality play in that logic. Second, it asks what kinds of cultural anxieties evolutionary theory raises and how evolutionary narratives negotiate them. Third, it examines the possibilities and limits of narrative transformation both as a historical phenomenon and as a theoretical question. This interdisciplinary dissertation is situated at the intersection of science studies, cultural studies, literary studies, and gender studies. Its understanding of science as a cultural practice that both emerges from and contributes to cultural expectations and institutional structures follows the tradition of science studies. Its focus on the question of popular appeal and the mechanisms of cultural change arises from cultural studies. Its view of narrative as a structural phenomenon is grounded in literary studies in general and feminist narrative theory in particular. Its understanding of gender and sexuality as implicated in discourses of epistemic authority builds on the view of gender and sexuality as contingent cultural categories central to gender studies. The primary material consists of over 25 British and American popular science books and novels, published roughly between 1990 and 2005. In order to highlight historical transformations, these texts are read in the context of Darwin s The Origin of Species and The Descent of Man, on the one hand, and such sociobiological classics as E. O. Wilson s On Human Nature and Richard Dawkins s The Selfish Gene, on the other. The research method combines feminist narrative analysis with cultural and historical contextualization, emphasizing discursive abruptions, recurrent narrative patterns, and underlying continuities. The dissertation demonstrates that the relationship between Darwin s evolutionary narrative and late twentieth-century evolutionary narratives is characterized by reemphasis, omissions, and continuous rewriting. In particular, contemporary evolutionary discourse extends the role assigned to reproduction both sexual and narrative in Darwin s writing, generating a narrative logic that imagines the desire to reproduce as the driving force of evolution and posits the reproductive sex act as the endlessly repeated narrative event that keeps the story going. The study argues that the popular appeal of evolutionary accounts of gender, sexuality, and human nature may arise, to an extent, from this reproductive narrative dynamic. This narrative dynamic, however, is not logically invulnerable. Since the continuation of the evolutionary narrative relies on successful reproduction, the possibility of reproductive failure poses a constant risk to narrative futurity, arousing cultural anxieties that evolutionary narratives need to address. The study argues that evolutionary narratives appease such anxieties by evoking a range of cultural narratives, especially romantic, religious, and national narratives. Furthermore, the study shows that the event-based logic of evolutionary narratives privileges observable acts over emotions, pleasures, identities, and desires, thus engendering a set of conceptual exclusions that limits the imaginative scope of evolution as a cultural narrative.

Models of Dispersal and Diversification

Ecology and evolutionary biology is the study of life on this planet. One of the many methods applied to answering the great diversity of questions regarding the lives and characteristics of individual organisms, is the utilization of mathematical models. Such models are used in a wide variety of ways. Some help us to reason, functioning as aids to, or substitutes for, our own fallible logic, thus making argumentation and thinking clearer. Models which help our reasoning can lead to conceptual clarification; by expressing ideas in algebraic terms, the relationship between different concepts become clearer. Other mathematical models are used to better understand yet more complicated models, or to develop mathematical tools for their analysis. Though helping us to reason and being used as tools in the craftmanship of science, many models do not tell us much about the real biological phenomena we are, at least initially, interested in. The main reason for this is that any mathematical model is a simplification of the real world, reducing the complexity and variety of interactions and idiosynchracies of individual organisms. What such models can tell us, however, both is and has been very valuable throughout the history of ecology and evolution. Minimally, a model simplifying the complex world can tell us that in principle, the patterns produced in a model could also be produced in the real world. We can never know how different a simplified mathematical representation is from the real world, but the similarity models do strive for, gives us confidence that their results could apply. This thesis deals with a variety of different models, used for different purposes. One model deals with how one can measure and analyse invasions; the expanding phase of invasive species. Earlier analyses claims to have shown that such invasions can be a regulated phenomena, that higher invasion speeds at a given point in time will lead to a reduction in speed. Two simple mathematical models show that analysis on this particular measure of invasion speed need not be evidence of regulation. In the context of dispersal evolution, two models acting as proof-of-principle are presented. Parent-offspring conflict emerges when there are different evolutionary optima for adaptive behavior for parents and offspring. We show that the evolution of dispersal distances can entail such a conflict, and that under parental control of dispersal (as, for example, in higher plants) wider dispersal kernels are optimal. We also show that dispersal homeostasis can be optimal; in a setting where dispersal decisions (to leave or stay in a natal patch) are made, strategies that divide their seeds or eggs into fractions that disperse or not, as opposed to randomized for each seed, can prevail. We also present a model of the evolution of bet-hedging strategies; evolutionary adaptations that occur despite their fitness, on average, being lower than a competing strategy. Such strategies can win in the long run because they have a reduced variance in fitness coupled with a reduction in mean fitness, and fitness is of a multiplicative nature across generations, and therefore sensitive to variability. This model is used for conceptual clarification; by developing a population genetical model with uncertain fitness and expressing genotypic variance in fitness as a product between individual level variance and correlations between individuals of a genotype. We arrive at expressions that intuitively reflect two of the main categorizations of bet-hedging strategies; conservative vs diversifying and within- vs between-generation bet hedging. In addition, this model shows that these divisions in fact are false dichotomies.